Hi Morgan! There are ab exercises I use that don't require sitting on the tailbone, although I'm not sure how far your pain radiates.

Here they are (they don't involve kneeling or standing, though):

-Lie on your back, with your legs bent and lifted, preferably with your lower legs on a chair, or something else that's the right height. Squeeze and lift your upper body (like a crunch), hold for a second or two, and lower. This works primarily the lower abs.

-Lie on your back, with both legs bent (as before), only without a chair, and straighten them so they're at roughly a 45 degree angle with the floor. This one is versatile--you can either just hold them there, or lift and lower them. Works most of the abs, but the upper abs more.

-Lie on your back with your legs straight out in front of you. Lift legs, keeping them straight (not locked straight--soft straight), to about a 60 degree angle with the floor. Hold a second or two, and lower. You may want to hold onto something with your arms above your head to keep your upper body down. This works the upper abs.

-Lie on your side, supporting your upper body with one elbow, and squeeze sideways, hold for a second or two, and repeat. This works the obliques.

Here's one that doesn't require being on your back: get on your front, put your elbows below your shoulders, and support the lower half on your toes. It's a little like push-up position, except you're on your elbows. You can either clasp your hands together or hold them in fists side-by-side, or whatever else feels comfortable. Keep your body straight (you'll need all your trunk muscles for this) and hold for as long as you can.

I don't know if there's anything in there that you can use, but hopefully there's something. There may be a bunch of Pilates moves that would work for you, though you would probably have to modify some a bit.

Good luck!